%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:36:10 EDT 2022
% Result : Unsatisfiable 1.97s 2.17s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of clauses : 108 ( 59 unt; 0 nHn; 54 RR)
% Number of literals : 178 ( 177 equ; 72 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 147 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(i_definition,axiom,
apply(i,X) = X ).
cnf(weak_fixed_point,axiom,
weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) ).
cnf(prove_weak_fixed_point,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)) ).
cnf(refute_0_0,plain,
apply(apply(apply(s,X),apply(X_9,X)),Z) = apply(apply(X,Z),apply(apply(X_9,X),Z)),
inference(subst,[],[s_definition:[bind(Y,$fot(apply(X_9,X)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(s,s),X_9),X) = apply(apply(s,X),apply(X_9,X)),
inference(subst,[],[s_definition:[bind(X,$fot(s)),bind(Y,$fot(X_9)),bind(Z,$fot(X))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( apply(apply(apply(s,s),X_9),X) != apply(apply(s,X),apply(X_9,X))
| apply(apply(s,X),apply(X_9,X)) = apply(apply(apply(s,s),X_9),X) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(s,s),X_9),X))),bind(Y0,$fot(apply(apply(s,X),apply(X_9,X))))]]) ).
cnf(refute_0_6,plain,
apply(apply(s,X),apply(X_9,X)) = apply(apply(apply(s,s),X_9),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,s),X_9),X),apply(apply(s,X),apply(X_9,X))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(s,X),apply(X_9,X)),Z) != apply(apply(X,Z),apply(apply(X_9,X),Z))
| apply(apply(s,X),apply(X_9,X)) != apply(apply(apply(s,s),X_9),X)
| apply(apply(apply(apply(s,s),X_9),X),Z) = apply(apply(X,Z),apply(apply(X_9,X),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,X),apply(X_9,X)),Z),apply(apply(X,Z),apply(apply(X_9,X),Z))) ),[0,0],$fot(apply(apply(apply(s,s),X_9),X))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(s,X),apply(X_9,X)),Z) != apply(apply(X,Z),apply(apply(X_9,X),Z))
| apply(apply(apply(apply(s,s),X_9),X),Z) = apply(apply(X,Z),apply(apply(X_9,X),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(s,X),apply(X_9,X)),apply(apply(apply(s,s),X_9),X)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(apply(s,s),X_9),X),Z) = apply(apply(X,Z),apply(apply(X_9,X),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X),apply(X_9,X)),Z),apply(apply(X,Z),apply(apply(X_9,X),Z))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)),
inference(subst,[],[refute_0_9:[bind(X,$fot(apply(s,apply(b,X_19)))),bind(Z,$fot(i)),bind(X_9,$fot(i))]]) ).
cnf(refute_0_11,plain,
apply(apply(apply(s,i),X_9),X_10) = apply(apply(i,X_10),apply(X_9,X_10)),
inference(subst,[],[s_definition:[bind(X,$fot(i)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_12,plain,
apply(i,X_10) = X_10,
inference(subst,[],[i_definition:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(s,i),X_9),X_10) != apply(apply(i,X_10),apply(X_9,X_10))
| apply(i,X_10) != X_10
| apply(apply(apply(s,i),X_9),X_10) = apply(X_10,apply(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,i),X_9),X_10),apply(apply(i,X_10),apply(X_9,X_10))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(s,i),X_9),X_10) != apply(apply(i,X_10),apply(X_9,X_10))
| apply(apply(apply(s,i),X_9),X_10) = apply(X_10,apply(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(apply(i,X_10),X_10) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(apply(s,i),X_9),X_10) = apply(X_10,apply(X_9,X_10)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),X_9),X_10),apply(apply(i,X_10),apply(X_9,X_10))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(apply(s,i),i),X_11) = apply(X_11,apply(i,X_11)),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(X_11)),bind(X_9,$fot(i))]]) ).
cnf(refute_0_17,plain,
apply(i,X_11) = X_11,
inference(subst,[],[i_definition:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(s,i),i),X_11) != apply(X_11,apply(i,X_11))
| apply(i,X_11) != X_11
| apply(apply(apply(s,i),i),X_11) = apply(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,i),i),X_11),apply(X_11,apply(i,X_11))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_19,plain,
( apply(apply(apply(s,i),i),X_11) != apply(X_11,apply(i,X_11))
| apply(apply(apply(s,i),i),X_11) = apply(X_11,X_11) ),
inference(resolve,[$cnf( $equal(apply(i,X_11),X_11) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(apply(s,i),i),X_11) = apply(X_11,X_11),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),X_11),apply(X_11,apply(i,X_11))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)),
inference(subst,[],[refute_0_20:[bind(X_11,$fot(apply(apply(s,apply(b,X_19)),i)))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(s,i),i),X_11) != apply(X_11,X_11)
| apply(X_11,X_11) = apply(apply(apply(s,i),i),X_11) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(s,i),i),X_11))),bind(Y0,$fot(apply(X_11,X_11)))]]) ).
cnf(refute_0_23,plain,
apply(X_11,X_11) = apply(apply(apply(s,i),i),X_11),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),X_11),apply(X_11,X_11)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)),
inference(subst,[],[refute_0_23:[bind(X_11,$fot(apply(apply(s,apply(b,X)),i)))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) != apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i))
| weak_fixed_point(X) != apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))
| weak_fixed_point(X) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)) ),
introduced(tautology,[equality,[$cnf( $equal(weak_fixed_point(X),apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) ),[1],$fot(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)))]]) ).
cnf(refute_0_26,plain,
( weak_fixed_point(X) != apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))
| weak_fixed_point(X) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
weak_fixed_point(X) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)),
inference(resolve,[$cnf( $equal(weak_fixed_point(X),apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) )],[weak_fixed_point,refute_0_26]) ).
cnf(refute_0_28,plain,
weak_fixed_point(X_19) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_29,plain,
( weak_fixed_point(X_19) != apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i))
| apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) = weak_fixed_point(X_19) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(weak_fixed_point(X_19))),bind(Y0,$fot(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i))))]]) ).
cnf(refute_0_30,plain,
apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) = weak_fixed_point(X_19),
inference(resolve,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))
| apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) != weak_fixed_point(X_19)
| weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))) ),[0],$fot(weak_fixed_point(X_19))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))
| weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),weak_fixed_point(X_19)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(s,Y),Y),Z) = apply(apply(Y,Z),apply(Y,Z)),
inference(subst,[],[s_definition:[bind(X,$fot(Y))]]) ).
cnf(refute_0_35,plain,
apply(apply(apply(s,X_8),i),X_10) = apply(apply(X_8,X_10),apply(i,X_10)),
inference(subst,[],[s_definition:[bind(X,$fot(X_8)),bind(Y,$fot(i)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_36,plain,
( apply(apply(apply(s,X_8),i),X_10) != apply(apply(X_8,X_10),apply(i,X_10))
| apply(i,X_10) != X_10
| apply(apply(apply(s,X_8),i),X_10) = apply(apply(X_8,X_10),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,X_8),i),X_10),apply(apply(X_8,X_10),apply(i,X_10))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(s,X_8),i),X_10) != apply(apply(X_8,X_10),apply(i,X_10))
| apply(apply(apply(s,X_8),i),X_10) = apply(apply(X_8,X_10),X_10) ),
inference(resolve,[$cnf( $equal(apply(i,X_10),X_10) )],[refute_0_12,refute_0_36]) ).
cnf(refute_0_38,plain,
apply(apply(apply(s,X_8),i),X_10) = apply(apply(X_8,X_10),X_10),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,X_8),i),X_10),apply(apply(X_8,X_10),apply(i,X_10))) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(s,s),i),Y) = apply(apply(s,Y),Y),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(Y)),bind(X_8,$fot(s))]]) ).
cnf(refute_0_40,plain,
( apply(apply(apply(s,s),i),Y) != apply(apply(s,Y),Y)
| apply(apply(s,Y),Y) = apply(apply(apply(s,s),i),Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(s,s),i),Y))),bind(Y0,$fot(apply(apply(s,Y),Y)))]]) ).
cnf(refute_0_41,plain,
apply(apply(s,Y),Y) = apply(apply(apply(s,s),i),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,s),i),Y),apply(apply(s,Y),Y)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( apply(apply(apply(s,Y),Y),Z) != apply(apply(Y,Z),apply(Y,Z))
| apply(apply(s,Y),Y) != apply(apply(apply(s,s),i),Y)
| apply(apply(apply(apply(s,s),i),Y),Z) = apply(apply(Y,Z),apply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,Y),Y),Z),apply(apply(Y,Z),apply(Y,Z))) ),[0,0],$fot(apply(apply(apply(s,s),i),Y))]]) ).
cnf(refute_0_43,plain,
( apply(apply(apply(s,Y),Y),Z) != apply(apply(Y,Z),apply(Y,Z))
| apply(apply(apply(apply(s,s),i),Y),Z) = apply(apply(Y,Z),apply(Y,Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(s,Y),Y),apply(apply(apply(s,s),i),Y)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(apply(apply(apply(s,s),i),Y),Z) = apply(apply(Y,Z),apply(Y,Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,Y),Y),Z),apply(apply(Y,Z),apply(Y,Z))) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(apply(s,s),i),Y),Z) != apply(apply(Y,Z),apply(Y,Z))
| apply(apply(Y,Z),apply(Y,Z)) = apply(apply(apply(apply(s,s),i),Y),Z) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(apply(s,s),i),Y),Z))),bind(Y0,$fot(apply(apply(Y,Z),apply(Y,Z))))]]) ).
cnf(refute_0_46,plain,
apply(apply(Y,Z),apply(Y,Z)) = apply(apply(apply(apply(s,s),i),Y),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,s),i),Y),Z),apply(apply(Y,Z),apply(Y,Z))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)) = apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i),
inference(subst,[],[refute_0_46:[bind(Y,$fot(apply(s,apply(b,X_19)))),bind(Z,$fot(i))]]) ).
cnf(refute_0_48,plain,
( apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)) != apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i)
| weak_fixed_point(X_19) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))
| weak_fixed_point(X_19) = apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) ),
introduced(tautology,[equality,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))) ),[1],$fot(apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i))]]) ).
cnf(refute_0_49,plain,
( weak_fixed_point(X_19) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))
| weak_fixed_point(X_19) = apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i)),apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
weak_fixed_point(X_19) = apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i),
inference(resolve,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(s,apply(b,X_19)),i))) )],[refute_0_33,refute_0_49]) ).
cnf(refute_0_51,plain,
( weak_fixed_point(X_19) != apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i)
| apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) = weak_fixed_point(X_19) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(weak_fixed_point(X_19))),bind(Y0,$fot(apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i)))]]) ).
cnf(refute_0_52,plain,
apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) = weak_fixed_point(X_19),
inference(resolve,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))
| apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) != weak_fixed_point(X_19)
| weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))) ),[0],$fot(weak_fixed_point(X_19))]]) ).
cnf(refute_0_54,plain,
( apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))
| weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i),weak_fixed_point(X_19)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
weak_fixed_point(X_19) = apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,s),i),apply(s,apply(b,X_19))),i),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))) )],[refute_0_10,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(i,apply(s,apply(b,X_19))) = apply(s,apply(b,X_19)),
inference(subst,[],[i_definition:[bind(X,$fot(apply(s,apply(b,X_19))))]]) ).
cnf(refute_0_57,plain,
apply(apply(i,apply(s,apply(b,X_19))),i) = apply(apply(i,apply(s,apply(b,X_19))),i),
introduced(tautology,[refl,[$fot(apply(apply(i,apply(s,apply(b,X_19))),i))]]) ).
cnf(refute_0_58,plain,
( apply(apply(i,apply(s,apply(b,X_19))),i) != apply(apply(i,apply(s,apply(b,X_19))),i)
| apply(i,apply(s,apply(b,X_19))) != apply(s,apply(b,X_19))
| apply(apply(i,apply(s,apply(b,X_19))),i) = apply(apply(s,apply(b,X_19)),i) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(i,apply(s,apply(b,X_19))),i),apply(apply(i,apply(s,apply(b,X_19))),i)) ),[1,0],$fot(apply(s,apply(b,X_19)))]]) ).
cnf(refute_0_59,plain,
( apply(i,apply(s,apply(b,X_19))) != apply(s,apply(b,X_19))
| apply(apply(i,apply(s,apply(b,X_19))),i) = apply(apply(s,apply(b,X_19)),i) ),
inference(resolve,[$cnf( $equal(apply(apply(i,apply(s,apply(b,X_19))),i),apply(apply(i,apply(s,apply(b,X_19))),i)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
apply(apply(i,apply(s,apply(b,X_19))),i) = apply(apply(s,apply(b,X_19)),i),
inference(resolve,[$cnf( $equal(apply(i,apply(s,apply(b,X_19))),apply(s,apply(b,X_19))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)),
introduced(tautology,[refl,[$fot(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))]]) ).
cnf(refute_0_62,plain,
( apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))
| apply(apply(i,apply(s,apply(b,X_19))),i) != apply(apply(s,apply(b,X_19)),i)
| apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)),apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) ),[1,1],$fot(apply(apply(s,apply(b,X_19)),i))]]) ).
cnf(refute_0_63,plain,
( apply(apply(i,apply(s,apply(b,X_19))),i) != apply(apply(s,apply(b,X_19)),i)
| apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)),apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),
inference(resolve,[$cnf( $equal(apply(apply(i,apply(s,apply(b,X_19))),i),apply(apply(s,apply(b,X_19)),i)) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_66,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_65]) ).
cnf(refute_0_67,plain,
( apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i))
| apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) != weak_fixed_point(X_19)
| apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = weak_fixed_point(X_19) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))),bind(Y0,$fot(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)))),bind(Z0,$fot(weak_fixed_point(X_19)))]]) ).
cnf(refute_0_68,plain,
( apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)) != weak_fixed_point(X_19)
| apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = weak_fixed_point(X_19) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)),apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = weak_fixed_point(X_19),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X_19)),i)),weak_fixed_point(X_19)) )],[refute_0_30,refute_0_68]) ).
cnf(refute_0_70,plain,
apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) = apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))),
introduced(tautology,[refl,[$fot(apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))))]]) ).
cnf(refute_0_71,plain,
( apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) != apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))
| apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != weak_fixed_point(X_19)
| apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) = apply(X_19,weak_fixed_point(X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))),apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))) ),[1,1],$fot(weak_fixed_point(X_19))]]) ).
cnf(refute_0_72,plain,
( apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != weak_fixed_point(X_19)
| apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) = apply(X_19,weak_fixed_point(X_19)) ),
inference(resolve,[$cnf( $equal(apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))),apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) = apply(X_19,weak_fixed_point(X_19)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)),weak_fixed_point(X_19)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
apply(apply(apply(b,X),Z),Z) = apply(X,apply(Z,Z)),
inference(subst,[],[b_definition:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_75,plain,
apply(apply(apply(s,apply(b,X)),i),Z) = apply(apply(apply(b,X),Z),Z),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(Z)),bind(X_8,$fot(apply(b,X)))]]) ).
cnf(refute_0_76,plain,
( apply(apply(apply(s,apply(b,X)),i),Z) != apply(apply(apply(b,X),Z),Z)
| apply(apply(apply(b,X),Z),Z) = apply(apply(apply(s,apply(b,X)),i),Z) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(s,apply(b,X)),i),Z))),bind(Y0,$fot(apply(apply(apply(b,X),Z),Z)))]]) ).
cnf(refute_0_77,plain,
apply(apply(apply(b,X),Z),Z) = apply(apply(apply(s,apply(b,X)),i),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X)),i),Z),apply(apply(apply(b,X),Z),Z)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( apply(apply(apply(b,X),Z),Z) != apply(X,apply(Z,Z))
| apply(apply(apply(b,X),Z),Z) != apply(apply(apply(s,apply(b,X)),i),Z)
| apply(apply(apply(s,apply(b,X)),i),Z) = apply(X,apply(Z,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),Z),Z),apply(X,apply(Z,Z))) ),[0],$fot(apply(apply(apply(s,apply(b,X)),i),Z))]]) ).
cnf(refute_0_79,plain,
( apply(apply(apply(b,X),Z),Z) != apply(X,apply(Z,Z))
| apply(apply(apply(s,apply(b,X)),i),Z) = apply(X,apply(Z,Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Z),Z),apply(apply(apply(s,apply(b,X)),i),Z)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
apply(apply(apply(s,apply(b,X)),i),Z) = apply(X,apply(Z,Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Z),Z),apply(X,apply(Z,Z))) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
apply(apply(apply(s,apply(b,X_29)),i),X_30) = apply(X_29,apply(X_30,X_30)),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_29)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_82,plain,
apply(apply(apply(s,i),i),X_30) = apply(X_30,X_30),
inference(subst,[],[refute_0_20:[bind(X_11,$fot(X_30))]]) ).
cnf(refute_0_83,plain,
( apply(apply(apply(s,i),i),X_30) != apply(X_30,X_30)
| apply(X_30,X_30) = apply(apply(apply(s,i),i),X_30) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(apply(s,i),i),X_30))),bind(Y0,$fot(apply(X_30,X_30)))]]) ).
cnf(refute_0_84,plain,
apply(X_30,X_30) = apply(apply(apply(s,i),i),X_30),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,i),i),X_30),apply(X_30,X_30)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( apply(X_30,X_30) != apply(apply(apply(s,i),i),X_30)
| apply(apply(apply(s,apply(b,X_29)),i),X_30) != apply(X_29,apply(X_30,X_30))
| apply(apply(apply(s,apply(b,X_29)),i),X_30) = apply(X_29,apply(apply(apply(s,i),i),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,apply(b,X_29)),i),X_30),apply(X_29,apply(X_30,X_30))) ),[1,1],$fot(apply(apply(apply(s,i),i),X_30))]]) ).
cnf(refute_0_86,plain,
( apply(apply(apply(s,apply(b,X_29)),i),X_30) != apply(X_29,apply(X_30,X_30))
| apply(apply(apply(s,apply(b,X_29)),i),X_30) = apply(X_29,apply(apply(apply(s,i),i),X_30)) ),
inference(resolve,[$cnf( $equal(apply(X_30,X_30),apply(apply(apply(s,i),i),X_30)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
apply(apply(apply(s,apply(b,X_29)),i),X_30) = apply(X_29,apply(apply(apply(s,i),i),X_30)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X_29)),i),X_30),apply(X_29,apply(X_30,X_30))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))),
inference(subst,[],[refute_0_87:[bind(X_29,$fot(X_19)),bind(X_30,$fot(apply(apply(i,apply(s,apply(b,X_19))),i)))]]) ).
cnf(refute_0_89,plain,
( apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) != apply(X_19,weak_fixed_point(X_19))
| apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))
| apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(X_19,weak_fixed_point(X_19)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)))),bind(Y0,$fot(apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))))),bind(Z0,$fot(apply(X_19,weak_fixed_point(X_19))))]]) ).
cnf(refute_0_90,plain,
( apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))) != apply(X_19,weak_fixed_point(X_19))
| apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(X_19,weak_fixed_point(X_19)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)),apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) = apply(X_19,weak_fixed_point(X_19)),
inference(resolve,[$cnf( $equal(apply(X_19,apply(apply(apply(s,i),i),apply(apply(i,apply(s,apply(b,X_19))),i))),apply(X_19,weak_fixed_point(X_19))) )],[refute_0_73,refute_0_90]) ).
cnf(refute_0_92,plain,
( apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)) != apply(X_19,weak_fixed_point(X_19))
| weak_fixed_point(X_19) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))
| weak_fixed_point(X_19) = apply(X_19,weak_fixed_point(X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))) ),[1],$fot(apply(X_19,weak_fixed_point(X_19)))]]) ).
cnf(refute_0_93,plain,
( weak_fixed_point(X_19) != apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))
| weak_fixed_point(X_19) = apply(X_19,weak_fixed_point(X_19)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i)),apply(X_19,weak_fixed_point(X_19))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
weak_fixed_point(X_19) = apply(X_19,weak_fixed_point(X_19)),
inference(resolve,[$cnf( $equal(weak_fixed_point(X_19),apply(apply(apply(s,apply(b,X_19)),i),apply(apply(i,apply(s,apply(b,X_19))),i))) )],[refute_0_55,refute_0_93]) ).
cnf(refute_0_95,plain,
( weak_fixed_point(X_19) != apply(X_19,weak_fixed_point(X_19))
| apply(X_19,weak_fixed_point(X_19)) = weak_fixed_point(X_19) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(weak_fixed_point(X_19))),bind(Y0,$fot(apply(X_19,weak_fixed_point(X_19))))]]) ).
cnf(refute_0_96,plain,
apply(X_19,weak_fixed_point(X_19)) = weak_fixed_point(X_19),
inference(resolve,[$cnf( $equal(weak_fixed_point(X_19),apply(X_19,weak_fixed_point(X_19))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
apply(fixed_pt,weak_fixed_point(fixed_pt)) = weak_fixed_point(fixed_pt),
inference(subst,[],[refute_0_96:[bind(X_19,$fot(fixed_pt))]]) ).
cnf(refute_0_98,plain,
( apply(fixed_pt,weak_fixed_point(fixed_pt)) != weak_fixed_point(fixed_pt)
| weak_fixed_point(fixed_pt) != weak_fixed_point(fixed_pt)
| weak_fixed_point(fixed_pt) = apply(fixed_pt,weak_fixed_point(fixed_pt)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(weak_fixed_point(fixed_pt),apply(fixed_pt,weak_fixed_point(fixed_pt))) ),[1],$fot(weak_fixed_point(fixed_pt))]]) ).
cnf(refute_0_99,plain,
( weak_fixed_point(fixed_pt) != weak_fixed_point(fixed_pt)
| weak_fixed_point(fixed_pt) = apply(fixed_pt,weak_fixed_point(fixed_pt)) ),
inference(resolve,[$cnf( $equal(apply(fixed_pt,weak_fixed_point(fixed_pt)),weak_fixed_point(fixed_pt)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
weak_fixed_point(fixed_pt) != weak_fixed_point(fixed_pt),
inference(resolve,[$cnf( $equal(weak_fixed_point(fixed_pt),apply(fixed_pt,weak_fixed_point(fixed_pt))) )],[refute_0_99,prove_weak_fixed_point]) ).
cnf(refute_0_101,plain,
weak_fixed_point(fixed_pt) = weak_fixed_point(fixed_pt),
introduced(tautology,[refl,[$fot(weak_fixed_point(fixed_pt))]]) ).
cnf(refute_0_102,plain,
$false,
inference(resolve,[$cnf( $equal(weak_fixed_point(fixed_pt),weak_fixed_point(fixed_pt)) )],[refute_0_101,refute_0_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.02/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Tue May 31 07:58:28 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.97/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.97/2.17
% 1.97/2.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.97/2.18
%------------------------------------------------------------------------------